If '+' means 'x', '÷' means '-', '-' means '+', and 'x' means '÷'. Which of the following will be the value of the expression? $12+5-24\times3 \div 5$
Expression Evaluation with Symbol Substitution
This solution explains how to solve the given mathematical expression by replacing operators according to the defined rules and then evaluating the result using the standard order of operations.
Symbol Replacements Defined
The problem provides a set of rules for symbol substitution:
| Original Symbol | Replacement Symbol |
|---|---|
| + | × |
| ÷ | - |
| - | + |
| × | ÷ |
Applying Operator Changes
The original expression is $12+5-24\times3 \div 5$. Applying the substitution rules yields a new expression:
- The '+' sign is replaced by '×'.
- The '-' sign is replaced by '+'.
- The '×' sign is replaced by '÷'.
- The '÷' sign is replaced by '-'.
Therefore, the expression transforms into: $12 \times 5 + 24 \div 3 - 5$
Evaluating the New Expression
The modified expression $12 \times 5 + 24 \div 3 - 5$ is evaluated using the order of operations (BODMAS/PEMDAS):
- Division: Perform the division first.
$24 \div 3 = 8$
The expression becomes: $12 \times 5 + 8 - 5$ - Multiplication: Next, perform the multiplication.
$12 \times 5 = 60$
The expression simplifies to: $60 + 8 - 5$ - Addition: Perform the addition.
$60 + 8 = 68$
The expression is now: $68 - 5$ - Subtraction: Finally, perform the subtraction.
$68 - 5 = 63$
The value of the evaluated expression is 63.
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
